Quantum electrodynamic corrections for molecules: Vacuum polarisation and electron self energy in a two-component relativistic framework

TL;DR

This paper implements quantum electrodynamic corrections, specifically vacuum polarisation and electron self energy, within a two-component relativistic framework to improve accuracy in molecular and atomic calculations.

Contribution

It introduces a method to evaluate QED corrections using a two-component ZORA framework, demonstrating efficiency and agreement with four-component results.

Findings

QED corrections can be accurately computed in a two-component framework.

The method shows excellent agreement with four-component calculations.

QED effects significantly impact ionisation and transition energies.

Abstract

Vacuum polarisation (VP) and electron self energy (SE) are implemented and evaluated as quantum electrodynamic (QED) corrections in a (quasi-relativistic) two-component zeroth order regular approximation (ZORA) framework. For VP, the Uehling potential is considered, and for SE, the effective potentials proposed by Flambaum and Ginges as well as the one proposed by Pyykk\"o and Zhao. QED contributions to ionisation energies of various atoms and group 2 monofluorides, group 1 and 11 valence orbital energies, $^2\mathrm{P}_{1/2} \leftarrow {}^{2}\mathrm{S}_{1/2}$ and $^{2}\mathrm{P}_{3/2} \leftarrow {}^{2}\mathrm{S}_{1/2}$ transition energies of Li-, Na-, and Cu-like ions of nuclear charge $Z$ = 10, 20, ..., 90 as well as $\Pi_{1/2}\leftarrow \Sigma_{1/2}$ and $\Pi_{3/2}\leftarrow\Sigma_{1/2}$ transition energies of BaF and RaF are presented. Furthermore, perturbative and self-consistent treatments of QED corrections are compared for Kohn--Sham orbital energies of gold. It is demonstrated, that QED corrections can be obtained in a two-component ZORA framework efficiently and in excellent agreement with corresponding four-component results.